A168228 Coefficient triangle sequence of characteristic polynomials of a Fermat like matrix:M(n)=Pascal n-th matrix: F(n)=Inverse[Transpose[M(n)]].M(n)

1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 0, 1, 1, 1, -5, 10, -10, 5, -1, 1, -5, -4, 25, -4, -5, 1, 1, 15, 64, 50, -50, -64, -15, -1, 1, 15, 65, 66, 30, 66, 65, 15, 1, 1, -55, 455, -671, 1410, -1410, 671, -455, 55, -1, 1, -55, 1815, -4730, 11495, -7251, 11495, -4730, 1815, -55

Offset

0,17

Comments

Row sums are:

{1, 0, 1, 0, 4, 0, 9, 0, 324, 0, 9801, 0,...}

Example Matrix F(3):

{{1, 1, 1},

{-1, -3, -2},

{1, 2, 1}}

References

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 172.

Links

Table of n, a(n) for n=0..64.

Example

{1},
{1, -1},
{1, -1, 1},
{1, 1, -1, -1},
{1, 1, 0, 1, 1},
{1, -5, 10, -10, 5, -1},
{1, -5, -4, 25, -4, -5, 1},
{1, 15, 64, 50, -50, -64, -15, -1},
{1, 15, 65, 66, 30, 66, 65, 15, 1},
{1, -55, 455, -671, 1410, -1410, 671, -455, 55, -1},
{1, -55, 1815, -4730, 11495, -7251, 11495, -4730, 1815, -55, 1},
{1, 197, 4675, -33825, -54978, 99174, -99174, 54978, 33825, -4675, -197, -1}

Mathematica

Clear[T, M, F];
T[n_, m_] := If[n >= m, Binomial[n, m], 0];
M[n_] := Table[T[k, m], {k, 0, n}, {m, 0, n}];
F[n_] := Inverse[Transpose[M[n]]].M[n];
Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[F[n], x], x], {n, 0, 10}]];
Flatten[%]

Crossrefs

A045912

Sequence in context: A001483 A173679 A230208 * A277950 A087109 A063261

Adjacent sequences: A168225 A168226 A168227 * A168229 A168230 A168231

Keyword

sign,uned

Author

Roger L. Bagula, Nov 20 2009

Status

approved